DEFECTS IN CRYSTALS

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DEFECTS IN CRYSTALS

• Point defects
• Line defects
• Surface Imperfections

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PROPERTIES
Structure sensitive
Structure Insensitive
E.g. Density, elastic modulus
E.g. Yield stress,
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CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
3D(Volume defects)
1D(Line defects)
2D(Surface / Interface)
0D(Point defects)
Twins
Surface
Vacancy
Dislocation
Interphaseboundary
Precipitate
Disclination
Impurity
Faultedregion
Frenkeldefect
Dispiration
Grainboundary
Voids / Cracks
Twinboundary
Schottkydefect
Stackingfaults
Thermalvibration
Anti-phaseboundaries
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SYMMETRY ASSOCIATED DEFECTS
Screw
Translation
Rotation
AtomicLevel
Dislocation
Disclination
Dispiration
SYMMETRY ASSOCIATED DEFECTS
Inversion
Mirror
Rotation
Twins
Multi-atom
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Based on origin
DEFECTS
Random
Structural
Based on position
DEFECTS
Random
Ordered
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THE ENTITY IN QUESTION
GEOMETRICAL
PHYSICAL
E.g. spin, magnetic moment
E.g. atoms, clusters etc.
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Vacancy
Interstitial
Non-ioniccrystals
Impurity
Substitutional
0D(Point defects)
Frenkel defect
Ioniccrystals
Other
Schottky defect

• Imperfect point-like regions in the crystal
  about the size of 1-2 atomic diameters

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Vacancy

• Missing atom from an atomic site
• Atoms around the vacancy displaced
• Tensile stress field produced in the vicinity

Tensile StressFields ?
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Relativesize
Interstitial
Compressive StressFields
Impurity
Substitutional
Compressive stress fields

• SUBSTITUTIONAL IMPURITY ? Foreign atom
  replacing the parent atom in the crystal ?
  E.g. Cu sitting in the lattice site of FCC-Ni
• INTERSTITIAL IMPURITY ? Foreign atom
  sitting in the void of a crystal ? E.g. C
  sitting in the octahedral void in HT FCC-Fe

Tensile StressFields
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Interstitial C sitting in the octahedral void in
HT FCC-Fe

• rOctahedral void / rFCC atom 0.414
• rFe-FCC 1.29 Å ? rOctahedral void 0.414 x
  1.29 0.53 Å
• rC 0.71 Å
• ? Compressive strains around the C atom
• Solubility limited to 2 wt (9.3 at)

Interstitial C sitting in the octahedral void in
LT BCC-Fe

• rTetrahedral void / rBCC atom 0.29 ? rC 0.71
  Å
• rFe-BCC 1.258 Å ? rTetrahedral void 0.29 x
  1.258 0.364 Å
• ? But C sits in smaller octahedral void-
  displaces fewer atoms
• ? Severe compressive strains around the C atom
• Solubility limited to 0.008 wt (0.037 at)

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ENTHALPY OF FORMATION OF VACANCIES

• Formation of a vacancy leads to missing bonds
  and distortion of the lattice
• The potential energy (Enthalpy) of the system
  increases
• Work required for the formaion of a point defect
  ? Enthalpy of formation (?Hf) kJ/mol or eV /
  defect
• Though it costs energy to form a vacancy its
  formation leads to increase in configurational
  entropy
• ? above zero Kelvin there is an equilibrium
  number of vacancies

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• Let n be the number of vacancies, N the number
  of sites in the lattice
• Assume that concentration of vacancies is small
  i.e. n/N ltlt 1
• ? the interaction between vacancies can be
  ignored
• ? ?Hformation (n vacancies) n . ?Hformation (1
  vacancy)
• Let ?Hf be the enthalpy of formation of 1 mole
  of vacancies

?S ?Sthermal ?Sconfigurational
?G ?H ? T ?S
Larger contribution
?G (putting n vacancies) n?Hf ? T ?Sconfig
For minimum
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?
Assuming n ltlt N
Considering only configurational entropy
User R instead of k if ?Hf is in J/mole
?S ?Sthermal ?Sconfigurational
Using
Independent of temperature, value of 3
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• Certain equilibrium number of vacancies are
  preferred at T gt 0K

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Ionic Crystals

• Overall electrical neutrality has to be
  maintained

Frenkel defect

• Cation (being smaller get displaced to
  interstitial voids
• E.g. AgI, CaF2

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Schottky defect

• Pair of anion and cation vacancies
• E.g. Alkali halides

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Other defects due to charge balance

• If Cd2 replaces Na ? one cation vacancy is
  created

Defects due to off stiochiometry

• ZnO heated in Zn vapour ? ZnyO (y gt1)
• The excess cations occupy interstitial voids
• The electrons (2e?) released stay associated to
  the interstitial cation

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• FeO heated in oxygen atmosphere ? FexO (x lt1)
• Vacant cation sites are present
• Charge is compensated by conversion of ferrous
  to ferric ion
• Fe2 ? Fe3 e?
• For every vacancy (of Fe cation) two ferrous
  ions are converted to ferric ions ? provides
  the 2 electrons required by excess oxygen

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